Question

why is a force needed to keep a body moving over a circular path find a formula for a force acting on a body moving with uniform speed over a circular path

Answer 1

because force can need to keep a body moving and formula is product of mass and 2*22/7*r

Answer 2

Centripetal force is used to keep a body in a circular motion.

If a body moves with uniform speed in a circular path it keeps moving in accelerating motion due to change in direction and force acting on body towards centre of circular path known as centripetal force. Let the uniform speed of object be v and the mass be m moving in a path of circle of radius r.

Now we know F = ma  

Since path is circular, then the centripetal acceleration $a=\frac{v^{2}}{r}.$

The centripetal force is expressed as, $\bold{\mathrm{F}=\frac{m v^{2}}{r}}$